Courses

• CAS MA 381: Elementary Probability
  A calculus-based introductory course in probability. Language of probability, combinatorics, conditional probability, discrete and continuous random variables, the Poisson process, joint probability distribution, moment generating function, law of large numbers and central limit theorem, sample estimators for mean and variance. Cannot be taken for credit in addition to CAS MA 581.
• CAS MA 401: Senior Independent Work
  
• CAS MA 402: Senior Independent Work
  
• CAS MA 411: Advanced Calculus
  Extends concepts and techniques of calculus and develops further applications. Topics include higher dimensional calculus, applications of vector analysis, uniform convergence of series, complex series, improper integrals, gamma and beta functions, Stirling's formula, Fourier series and transform.
• CAS MA 412: Complex Variables
  Basic concepts, results, and applications of complex analysis. Emphasis on computation and applications. Complex plane and functions, differentiability, Cauchy-Riemann conditions, contour integrals, Cauchy formulas, complex series, residue calculus, applications. Extends the concepts of the calculus to the complex setting.
• CAS MA 416: Analysis of Variance
  Fundamental concepts and analytical skills in analysis of variance, including crossed and nested designs, as well as fixed- and random- effect models. Trend analysis for repeated measures, expected mean squares, and non-parametric techniques. SAS is used throughout the course.
• CAS MA 442: Honors Level Linear Algebra
  A thorough development of the fundamentals of linear algebra. Systems of linear equations; matrices, linear transformations, duality; determinants, characteristic and minimal polynomials; diagonalization and normal forms of linear transformations; inner products, unitary and self-adjoint operators, and spectral theory. Applications to physics, probability, and statistics. (Cannot be taken for credit in addition to CAS MA 242.)
• CAS MA 471: Chaotic Dynamical Systems
  Iteration of functions in one and higher dimensions. Periodic points; hyperbolicity; recurrence; topological conjugacy and structural stability; chaotic dynamics. Some numerical experimentation involving personal computers.
• CAS MA 491: Directed Study
  
• CAS MA 492: Directed Study
  
• CAS MA 505: History of Mathematics
  Patterns of mathematical thought from antiquity to the seventeenth century. Emphasis throughout on the background and origins of the mathematical revolution of the seventeenth century in which Descartes, Newton, and Leibniz played key roles.
• CAS MA 511: Introduction to Analysis I
  Fundamental concepts of mathematical reasoning. Properties of the real-number system, elementary point-set theory, metric spaces. Limits, sequences, series, convergence, uniform convergence, continuity. Differentiability for functions of a single variable, Riemann-Stieltjes integration.
• CAS MA 512: Introduction to Analysis II
  Background of CAS MA 511 used to develop further topics of calculus. Exponential and logarithmic functions, Taylor series, power series, real analytic functions. Differential and integral calculus for functions of several variables. Line and surface integrals, divergence theorem, Stokes's theorem, inverse and implicit function theorems, change of variables. Fourier analysis.
• CAS MA 528: Introduction to Modern Geometry
  The foundations of Euclidean geometry. Transformation and symmetries in the plane, inversive and projective planes, coordinates, conics and quadrics, the Golden Section, intermediary and Dedekind's axiom, models for non-Euclidean geometries.
• CAS MA 531: Mathematical Logic
  The syntax and semantics of sentential and quantificational logic, culminating in the Gödel Completeness Theorem. The Gödel Incompleteness Theorem and its ramifications for computability and philosophy. Also offered as CAS PH 461.
• CAS MA 532: Foundations of Mathematics
  Axiomatic set theory as a foundation for mathematics and as a field of mathematics: Axiom of Choice, the Continuum Hypothesis, and consistency results.
• CAS MA 539: Methods of Scientific Computing
  (Meets with CAS CS 539.) An introduction to topics including computational linear algebra, solutions of linear equations, numerical integration and solution of differential equations, finite element methods, and methods of stochastic simulation (i.e., Monte Carlo methods).
• CAS MA 541: Modern Algebra I
  Basic properties of groups, Sylow theorems, basic properties of rings and ideals, Euclidean rings, polynomial rings.
• CAS MA 542: Modern Algebra II
  Vector spaces and modules, Galois theory, linear transformations and matrices, canonical forms, bilinear and quadratic forms.
• CAS MA 555: Numerical Analysis I
  Numerical solutions of equations, iterative methods, analysis of sequences. Theory of interpolation and functional approximation, divided differences. Numerical differentiation and integration. Polynomial theory. Ordinary differential equations.

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